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Low-complexity computations for nilpotent subgroup problems

    https://doi.org/10.1142/S021819671950019XCited by:3 (Source: Crossref)

    We solve the following algorithmic problems using TC0 circuits, or in logspace and quasilinear time, uniformly in the class of nilpotent groups with bounded nilpotency class and rank: subgroup conjugacy, computing the normalizer and isolator of a subgroup, coset intersection, and computing the torsion subgroup. Additionally, if any input words are provided in compressed form as straight-line programs or in Mal’cev coordinates, the algorithms run in quartic time.

    Communicated by V. Diekert

    AMSC: 20F10, 20F18, 68Q25
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